I think the statement of the particular construction of a hierarchy being immaterial is wrong. Nearly every oppressive society in history have been patriarchal. The few societies that weren't were either matriarchal or without rigid gender roles. I don't know if there will ever be room for a "good trans person" in the republican party the way that there is room for "good black people." Being trans is considered an inherent abomination and white nationalism has never been more popular, afaik, than white supremacy in the USA.

Before trans people are recognized by the GOP they would need to abandon patriarchy. That won't happen. If it does the party would be so unrecognizable that it may as well be something entirely different.